Thanks to mitaliajgaonkar for helping find the solution. It involves editing the source code in the following way:

Navigate to where your Qlik Sense program files are, and find the file:

~\Qlik\Sense\Client\assets\hub\hub.js

Copy this file and save it somewhere else as a backup in case anything goes wrong. Then open the file and find the string tid="MenuBtn".

This string is in a <button> tag which you will need to delete as well as the <div> around the button. Once this has been removed you will no longer see the dropdown for Dev Hub, Help, and About on any account. Now, to get to the dev hub you just append "/dev-hub/" to the end of your url. Keep in mind that if you upgrade, you will have to redo this change.

I realize that even with hiding this button, the user can still type "/dev-hub/" at the end of the hub URL and have access to the dev hub anyway. Eventually I will need to figure out how to block access to this based on security rules or something.